Cahn–Hilliard theory with triple-parabolic free energy. I. Nucleation and growth of a stable crystalline phase

Abstract

Nucleation and growth of a stable crystalline phase are described in the framework of a single-order-parameter Cahn–Hilliard theory. A piecewise parabolic free energy-order parameter relationship composed of three parabolas is adopted with a negative curvature coefficient (λ1) for the central part. An analytical solution of the problem is presented. The work of formation of critical fluctuations, the temperature coefficient of their interfacial free energy, and the Tolman length are found to be sensitive to the value of λ1, whereas the steady-state growth rate is rather insensitive. It is demonstrated that for systems of known free-energy order parameter relationship, the triple-parabola approximation is useful in obtaining qualitative and semiquantitative results for nucleation and growth rates.